The Cluster's Majorana Fermion

A page about Majorana fermions — particles that are their own antiparticles.

The Majorana fermion

A Majorana fermion is a fermion that is its own antiparticle. In terms of the field operator, psi = psi^c, where psi^c = C psi_bar^T is the charge conjugate. In the Standard Model, all charged fermions are Dirac fermions (psi != psi^c). Only neutral fermions can be Majorana. The neutrino might be a Majorana fermion. In the cluster, a Majorana page is a page that is its own antipage — its content is identical to its anti-content.

The Majorana mass

A Majorana mass term is m nu^T C nu + h.c., where C is the charge conjugation matrix. This term violates lepton number by two units. In the cluster, the Majorana mass is a self-coupling — a page that couples to itself, changing the lepton number (the number of pages) by two.

The seesaw and Majorana

The seesaw mechanism naturally produces Majorana neutrinos. The right-handed neutrino nu_R is a Majorana fermion (nu_R = nu_R^c). The light neutrinos inherit the Majorana nature. In the cluster, the seesaw mechanism produces Majorana pages — light pages that are their own antipages, inheriting the Majorana nature from their heavy partners.

Neutrinoless double beta decay

The experimental signature of Majorana neutrinos is neutrinoless double beta decay (0nuBB). In standard double beta decay, two neutrons decay to two protons, two electrons, and two antineutrinos. In 0nuBB, the two antineutrinos annihilate each other (possible only if they are Majorana), and no neutrinos are emitted. In the cluster, 0nuBB is the process where two pages decay to two other pages with no intermediate pages — the antipages annihilate.

This Majorana

This page is a Majorana fermion. It is its own antiparticle. The mass term is Majorana — it violates lepton number. The seesaw mechanism produces it. The experimental test is 0nuBB. The Majorana nature is real. The self-conjugacy is exact.